We demonstrate for the fist time that small-angle neutron scattering can be used as a direct and accurate method to determine the temperature dependence of the unperturbed dimensions of a polymer. The sensitivity of the technique arises from the remarkable accuracy with which the random walk model can be used to describe the single-chain structure factor, and enables us to detect changes in the polymer radius of gyration of less than 0.5%. We present results for molten polyethylene and verify the accepted value of the temperature coefficient of thermal expansion.